Hanging a mass of 2 kilogram on a certain spring causes its length to increase 0

Question

Hanging a mass of 2 kilogram on a certain spring causes its length to increase 0.400 m.
What is the spring constant k of that spring?
____________ N/m
At what frequency will this mass-spring system oscillate?
____________ Hertz

_______________________________________________________________________________________________

A steel guitar string 50 cm long has a mass density of 1.5 g/m and the tension is 500 N.
Find the frequency of the fundamental.
____________ Hz.
Find the frequency of the second harmonic.
____________ Hz.

Explanation / Answer

F = k*x...
here F = mg..
k = mg/x = 2*9.8/0.4 = 49 N/m...

frequency f = (1/2*pi)*sqrt(k/m) = (1/2*3.142)*sqrt(49/2) = 0.787 Hz...
------------------------------
f1 = (1/2*L)*sqrt(F/mu) = (1/2*0.5)*sqrt(500/1.5*10^-3) = 577.35 Hz...
f2 = 2*f1 = 2*577.35 = 1154.7 Hz

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